Fundamentals of Medicinal Chemistry

H¼^12 VV

2

 1 =R 1 r 1 =R 2 rþV (5:8)

whereris the position of the electron. The use of the Hartree–Fock approxima-

tion reduces computer time and reduces the cost without losing too much in the

way of accuracy. Computer time may be further reduced by the use of semi-

empirical methods. These methods use experimentally determined data to sim-

plify many of the atomic orbitals, which in turn simplifies the Schrodinger

equation for the structure. Solving the Schrodinger equation uses a mathemat-

ical method, which is initially based on guessing a solution for each electrons

molecular orbital. The computer tests the accuracy of this trial solution and

based on its findings modifies the trial solution to produce a new solution. The

accuracy of this new solution is tested and a further solution is proposed by the

computer. This process is repeated until the testing the solution gives answers

within acceptable limits. In molecular modelling the solutions obtained by the

use of these methods describe the molecular orbitals of each electron in the

molecule. The solutions are normally in the form of sets of equations, which

may be interpretated in terms of the probability of finding an electron at specific

points in the structure. Graphics programs may be used to convert these prob-

abilities into either presentations like those shown in Figures 5.1 and 5.2 or into

electron distribution pictures (Figure 5.8). However, because of the computer

time involved, it is not feasible to deal with structures with more than several

hundred atoms, which makes the quantum mechanical approach less suitable for

large molecules such as the proteins that are of interest to medicinal chemists.

H N

HH

H

H

N

H

H

H

H

H

Pyrrole Pyrrole, orientation

in the model

Figure 5.8 The stick picture of pyrrole on which is superimposed the probability of finding

electrons at different points in the molecule obtained using quantum mechanics

Quantum mechanics is useful for calculating the values of ionization poten-

tials, electron affinities, heats of formation and dipole moments and other

physical properties of atoms and molecules. It can also be used to calculate

the relative probabilities of finding electrons (the electron density) in a structure

(Figure 5.8). This makes it possible to determine the most likely points at which

108 COMPUTER AIDED DRUG DESIGN